What is your answer to this Logic question? (Mine included)

[Ayushi160695]

Homework Statement

The rules for a certain frequent-flyer club include the following statements: "Any member who fails to earn any mileage during the first twelve months after enrollment in the program may be removed from the program. Except as otherwise provided, any member who fails at any time to earn mileage for a period of three consecutive years is subject to termination of his or her membership and forfeiture of all accrued mileage. Notwithstanding this provision, no pre-July 1 2014, member who has earned mileage ( other than enrollment bonus) prior to July 1, 2005, shall be subject under this provision to the termination of his or her membership and to the cancellation of mileage accrued prior to July 1 , 2005, until the amount of such mileage falls below 10,000 miles (the amount necessary for the lowest available award under the structure in place as of June 30, 2004), or until December 15, 2015, whichever comes first.

Homework Equations

Let x be a particular member of this club, and let
p= "x fails to earn mileage during the first twelve months after enrollment"
q= "x fails to earn mileage for a period of time of three consecutive years"
r= "x became a member prior to July 1, 2004"
s= "x currently has at least 100,000 miles for pre-July 1,2005,mileage (not including enrollment bonus miles)"
t= "the current date is prior to December 15, 2015"
Use symbols to write the complete condition under which x's membership may be terminated.

The Attempt at a Solution

My answer : [ (p V q) N ~r] V ( s V t) ( N means AND)
What do you think? What's yours?

 

[haruspex]

My solution looks quite different. For a start, it seems to me that condition p is sufficient in itself, so the answer should be of the form pV(...).

 

[Ayushi160695]

My solution looks quite different. For a start, it seems to me that condition p is sufficient in itself, so the answer should be of the form pV(...).

Can you please give your full answer so that I can derive a truth table? Thanks.

 

[haruspex]

Can you please give your full answer so that I can derive a truth table? Thanks.

This is a homework forum. We do not hand out complete answers.
Do you agree that condition p by itself is a sufficient condition? If so, please make another attempt.

 

[Ayushi160695]

This is a homework forum. We do not hand out complete answers.
Do you agree that condition p by itself is a sufficient condition? If so, please make another attempt.

Okay. I'm sorry. I'm new here.
No, I don't agree since even if p is true but the condition r is true as well then its condition r that matters not p. That is even if the person fails to earn any mileage during the first twelve months, if the person was a member prior to 1 July 2004, then her/his contract will not be terminated as per condition p, provided s or t are false as well.

 

[haruspex]

No, I don't agree since even if p is true but the condition r is true as well then its condition r that matters not p. That is even if the person fails to earn any mileage during the first twelve months, if the person was a member prior to 1 July 2004, then her/his contract will not be terminated as per condition p, provided s or t are false as well.

Then we read it differently. Here's how I read it. This first statement is absolute and not qualified by anything that comes later:

Any member who fails to earn any mileage during the first twelve months after enrollment in the program may be removed from the program.

The next statement gives a second reason for termination, but notes that there are some exceptions to this rule:

Except as otherwise provided, any member who fails at any time to earn mileage for a period of three consecutive years is subject to termination o

It then proceeds to describe the exceptions to "this provision":

Notwithstanding this provision,

 

[Ayushi160695]

Then we read it differently. Here's how I read it. This first statement is absolute and not qualified by anything that comes later:

The next statement gives a second reason for termination, but notes that there are some exceptions to this rule:

It then proceeds to describe the exceptions to "this provision":

I see. I believe you are right. Then my answer would be : p V [ (q N ~r) V ( s V t) ]
What do you think?

 

[haruspex]

I see. I believe you are right. Then my answer would be : p V [ (q N ~r) V ( s V t) ]
What do you think?

Ok, we now agree on what happens if p is true. So suppose it is false. For that case you have (q N ~r) V ( s V t). In particular, that says that s and t are each in themselves sufficient basis for termination. That is very odd since they actually contribute to reason for non-termination.

 

[Ayushi160695]

Ok, we now agree on what happens if p is true. So suppose it is false. For that case you have (q N ~r) V ( s V t). In particular, that says that s and t are each in themselves sufficient basis for termination. That is very odd since they actually contribute to reason for non-termination.

Indeed. If both s and t are false, then (s V t) = 0, and if r is false then then ~r is 1. It then depends on q, if q is true, they are terminated, else they are not terminated.
Another case where if s or t is true then ( s V t) = 1, and if r is false then ~r is 1. If q is true or false, they are terminated. But if r is true, then ~r is 0. If q is true or false, then they are terminated again. When q is false, even if r , s or t are true, they should not be terminated. which makes me think that p V [ (q N ~r) V ( s V t) ] is erroneous.

 

[haruspex]

p V [ (q N ~r) V ( s V t) ] is erroneous

Quite so. Any more ideas?